Optimal pitch angle for the blades of the HAWT
 

Dear All,

If anyone could assist me with following I would be very thankful.

My question is related to the optimal pitch angle when wind rotor blades are not moving.

The power extracted from the wind is equal to 0.5*rho*A*Cp(lambda)*velocity^3, where rho - air density, A - area of the rotor (pi*radius^2 for HAWTs, 2*radius*blade_height for VAWTs), Cp(lambda) - rotor power coefficient which shows the effectiveness of the turbine at specific lambda. Lambda is non-dimensional operator which shows the ratio of linear velocity of the blade which is angular_velocity*radius to the air velocity.

For each air velocity value there is a optimal angular velocity, so the wind rotor could operate at optimal lambda, thus to have maximum rotor power coefficient. It works just fine when wind rotor is spinning and blades have some linear velocity. Changing the pitch angle it is possible to change the angle of attack, so the rotor will either decelerate or accelerate.

Here comes the question:

if wind rotor is not spinning, so linear velocity equals to zero. If linear velocity is zero, than lambda is also zero - thus Cp(lambda) is zero. Which pitch angle the wind blades have to be set to, so they will start to rotate? I am more curious about twisted blades, since one pitch angle will result in different angles of attack along the length of the blade, because blade is twisted.

Thank you so much.